Synthesis of a Spatial SS Serial Chain for a Prescribed Acceleration Task

In this paper we formulate and solve the syn- thesis equations for an SS serial chain with a task that has at least one prescribed acceleration. The SS chain con- strains a point P in the moving body to lie on the surface of a sphere about a point B in the fixed body. We find that there are four basic tasks that meet this requirement that separate into two fundamental cases, whether one or two accelerations are specified. The two cases for polynomial synthesis equations are with slightly different monomial structures. The linear product structures for these polyno- mial systems yield root bounds of 30 and 38, respectively. Algebraic elimination procedure is presented for both cases of task, which is implemented using Mathematica. Exam- ples demonstrate the design process.